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arXiv · 2002.07523

Torus cannot collapse to a segment

Mikhail G. Katz
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Abstract

In earlier work, we analyzed the impossibility of codimension-one collapse for surfaces of negative Euler characteristic under the condition of a lower bound for the Gaussian curvature. Here we show that, under similar conditions, the torus cannot collapse to a segment. Unlike the torus, the Klein bottle can collapse to a segment; we show that in such a situation, the loops in a short basis for homology must stay a uniform distance apart.

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Mikhail G. Katz. 2020-02-18. Torus cannot collapse to a segment. https://doi.org/10.1007/s00022-020-0525-8

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